Work

Remarks on τ$\tau$‐tilted versions of the second Brauer–Thrall conjecture

Year: 2025

Type: article

Abstract: In this short note, we state a stable and a ‐reduced version of the second Brauer–Thrall conjecture. The former is a slight strengthening of a brick version of the second Brauer–Thrall conjecture raised by Mousavand and Schroll–Treffinger–Valdivieso. The latter is stated in terms of Geiß–Leclerc–Schröer's generically ‐reduced components and provides a geometric interpretation of a question of Demonet. It follows that the stable second Brauer–Thrall conjecture implies our ‐reduced second Brauer–Thrall conjecture. Finally, we prove the reversed implication for the class of ‐tame algebras recently introduced by Asai–Iyama.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.70048

Author: Calvin Pfeifer

Institutions: University of Southern Denmark, University of Cologne

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funders: Syddansk Universitet, European Research Council